## The Lesson

The greatest common factor is the largest factor that is common to two or more numbers.## Understanding the Greatest Common Factor

The numbers that multiply together to make another number are its factors.**2**is a factor of 4 because

**2**×

**2**= 4:

**2**and

**3**are factors of 6 because

**2**×

**3**= 6:

The greatest common factor is the largest number that is a factor for both numbers. In our example,

**2**is the greatest common factor.

Another way of thinking about a factor is as a number which divides exactly into another number.

**2**is the largest number that divides exactly into 4 and 6.

4 ÷ **2** = 2

6 ÷ **2** = 3

## What's in a Name?

The Greatest Common Factor (GCF) is so called because it is the largest (*greatest*) factor that is the same (

*common*) to the numbers. It may sometimes be called:

- Greatest Common Divisor (GCD)
- Highest Common Factor (HCF)